Quantum information Definition and 39 Discussions

Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both the technical definition in terms of Von Neumann entropy and the general computational term.
It is an interdisciplinary field that involves quantum mechanics, computer science, information theory, philosophy and cryptography among other fields. Its study is also relevant to disciplines such as cognitive science, psychology and neuroscience. Its main focus is in extracting information from matter at the microscopic scale. Observation in science is one of the most important ways of acquiring information and measurement is required in order to quantify the observation, making this crucial to the scientific method. In quantum mechanics, due to the uncertainty principle, non-commuting observables cannot be precisely measured simultaneously, as an eigenstate in one basis is not an eigenstate in the other basis. As both variables are not simultaneously well defined, a quantum state can never contain definitive information about both variables.Information is something that is encoded in the state of a quantum system, it is physical. While quantum mechanics deals with examining properties of matter at the microscopic level, quantum information science focuses on extracting information from those properties, and quantum computation manipulates and processes information – performs logical operations – using quantum information processing techniques.Quantum information, like classical information, can be processed using digital computers, transmitted from one location to another, manipulated with algorithms, and analyzed with computer science and mathematics. Just like the basic unit of classical information is the bit, quantum information deals with qubits. Quantum information can be measured using Von Neumann entropy.
Recently, the field of quantum computing has become an active research area because of the possibility to disrupt modern computation, communication, and cryptography.

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  1. Llukis

    I About quantum computing

    Hello to everyone, I would like to ask you to brief questions. The first one is whether you could recommend any pedagogical books on Quantum Information and Computation. I tried Nielsen and Chuang but I found it too dense for a beginner in the field. The second question is the following: to...
  2. S

    More Nobel prizes in quantum information?

    Alain Aspect, John Clauser & Anton Zeilinger have rightfully received the Nobel prize for their contributions to quantum information, as they were three of the main pioneers of quantum information. However, is it now impossible or very unlikely that other physicists working on this field (e.g...
  3. Arquimedes

    I What is the physical meaning of concurence (quantum information)?

    Hello, I am currently studying about entanglement on spin-1/2 chains and I was able to find some information about the mathematical point of view of concurrence but I can't understand the physical meaning of it . Can somebody help me, please?
  4. steve1763

    A Quantum linear code/ Dual Code (CSS) proof

  5. steve1763

    A Knill-Laflamme condition Shors code

    The K-L condition has projection operators onto the codespace for the error correction code, as I understand it. My confusion I think comes primarily from what exactly these projections are? As in, how would one find these projections for say, the Shor 9-qubit code?
  6. steve1763

    A Derivation of recovery channel for bit flip error

    In general, if R is the recovery channel of an error channel ε, with state ρ, then and according to these lecture slides, we get the final result highlighted in red for a bit flip error channel. I am simply asking how one reaches this final result. Thank you (a full-ish derivation can be found...
  7. llha

    I [Quantum Computing] Quantum Parallelism State Calculation

    Hi, I'm going through Nielsen and Chuang's Quantum Computation and Quantum Information textbook and I don't really understand this part about quantum parallelism: Shouldn't the resulting state be (1/sqrt(2^4)) * (|0, f(0)> + |0, f(1)> + |1, f(1)> + |1, f(0)>), since the resulting state would...
  8. I

    Maximal Shannon Entropy

    I have used the Lagrange multiplier way of answering. So I have set up the equation with the constraint that ## \sum_{x}^{} p(x) = 1## So I have: ##L(x,\lambda) = - \sum_{x}^{} p(x)log_{2}p(x) - \lambda(\sum_{x}^{} p(x) - 1) = 0## I am now supposed to take the partial derivatives with respect...
  9. Danny Boy

    A Quantum Ising model correlation function query

    In this paper, on quantum Ising model dynamics, they consider the Hamiltonian $$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$ and the correlation function $$\mathcal{G} = \langle \mathcal{T}_C(\hat{\sigma}^{a_n}_{j_n}(t_n^*)\cdot\cdot\cdot...
  10. P

    A Translating/encoding a continuous variable model into a qubit model

    I've read these two pages that discuss going from qubit to continuous variable - https://arxiv.org/abs/quant-ph/0008040 and https://arxiv.org/abs/1907.09832 . I'm curious if anyone knows some papers that discuss going the other way around? I.e. qubitizing a continuous variable model? Any insight...
  11. P

    A Question: Unambiguous discrimination between two non-orthogonal states

    Consider a VCSEL laser that emits photon pulses with Poisson distribution for the number of photons per pulse. The power of the VCSEL has been set low so the mean photon number "u" is u<1. Consider this photon pulses can take two non-orthogonal states of polarization (for example: state 0 with...
  12. E

    Measurements of GHZ state

    Here's what I think I understand: First off, the GHZ state ##|GHZ \rangle = \frac {|000\rangle+|111\rangle} {\sqrt 2}##, and ##\sigma_x## and ##\sigma_y## are the usual Pauli matrices, so the four operators are easy to calculate in Matlab. I'm thinking the expectation values of each operator...
  13. E

    Projective measurements of quantum processor

    Am I correct in thinking that the system measures the probability |<f|1>|^2 for some state <f|? Then the probabilities for each of the six states would be: |<0|1>|^2= 0 |<1|1>|^2= 1 |<+x|1>|^2= |(1/√2)|^2 = 1/2 |<-x|1>|^2= |(-1/√2)|^2 = 1/2 |<+y|1>|^2= |(-i/√2)|^2 = 1/2 |<-y|1>|^2= |(i/√2)|^2...
  14. E

    Qubit Operations

    Part a: Gate H X Y Z S T R_x R_y Theta pi pi pi pi pi/2 pi/4 pi/2 pi/2 n_alpha (1/sqrt(2))*(1,0,1) (1,0,0) (0,1,0) (0,0,1) (0,0,1) (0,0,1) (1,0,0) (0,1,0) Using the info from the table and equation 1, I find: U_H=(i/sqrt(2))*[1,1;1,-1] U_X=i*[0,1;1,0] U_Y=i*[0,-i;i,0] U_Z=i*[1,0;0,-1]...
  15. Johny Boy

    A Expectation Value of a Stabilizer

    Given that operator ##S_M##, which consists entirely of ##Y## and ##Z## Pauli operators, is a stabilizer of some graph state ##G## i.e. the eigenvalue equation is given as ##S_MG = G## (eigenvalue ##1##). In the paper 'Graph States as a Resource for Quantum Metrology' (page 3) it states that...
  16. Johny Boy

    A Reduced Graph States

    Reduced graph states are characterized as follows from page 46 of this paper: Proposition: Let ##A \subseteq V## be a subset of vertices for a graph ##G = (V,E)## and ##B = V\setminus A## the corresponding complement in ##V##. The reduced state ##\rho_{G}^{A}:= tr_{B}(|G\rangle\langle G|)## is...
  17. E

    A Applying a General Lorentz Boost to Multipartite Quantum State

    I would like to apply a General Lorentz Boost to some Multi-partite Quantum State. I have read several papers (like this) on the theory of boosting quantum states, but I have a hard time applying this theory to concrete examples. Let us take a ##|\Phi^+\rangle## Bell State as an example, and...
  18. F

    A Random Quantum Walk

    I am an undergraduate doing research on QC/QI. My current topic to learn is continuous-time quantum walks, but first I must learn the random quantum walk. That being said, I was wondering if someone could simply explain what a random quantum walk is and then explain how they could be useful with...
  19. I

    Programs Topics at the junction of AdS/CFT and quantum information

    I have been asked to draft a (informal) research proposal for a PhD thesis. I have some background in quantum information and my interests are leaning towards the AdS/CFT correspondence. I was wondering if you could suggest a few (preferably recent) theory papers at the junction of quantum...
  20. T

    A What is a 'Quantum Coherence'?

    I have recently been reading some stuff on quantum information in the physics literature which refers to 'a mechanism by which a measurement in A determines quantum coherences in B', where A and B are subsystems of a larger system. I am aware of the meaning of the terms 'decoherence' and...
  21. W

    Tensor Product of Hamiltonians

    ##U_1 \otimes U_2 = (1- i H_1 \ dt) \otimes (1- i H_2 \ dt)## We can write ## | \phi_i(t) > \ = U_i(t) | \phi_i(0)>## where i can be 1 or 2 depending on the subsystem. The ## U ##'s are unitary time evolution operators. Writing as tensor product we get ## |\phi_1 \phi_2> = (1- i H_1 \ dt) |...
  22. F

    A How to measure the first qubit in two qubit system? QC

    I was wondering how to measure the first or even the second qubit in a quantum computing system after for example a Hadamard Gate is applied to the system of these qubits: A|00>+B|01>+C|10>+D|11>? A mathematical and intuitive explanation would be nice, I am a undergraduate sophomore student...
  23. C

    I Beam Splitter Phase Shift

    I'm having trouble understanding the phase shift produced by a beam splitter. I seem to be finding conflicting information. I'm specifically looking to understand a 50/50 beam splitter where one side has a dielectric mirror, as shown in this figure from wikipedia: I understand the pi...
  24. R

    Programs Prospects of Pursuing Graduate Studies in Quantum Computing

    Hello, I am close to finishing my undergraduate degree in Computer Engineering, and I am very interested in pursuing graduate studies. For a long time, I have been passionate about computer science and I've been looking into the research done in various labs in the schools that I'm considering...
  25. D

    Finding the magnetization in nuclear magnetic resonance

    Homework Statement J-coupling term between two spins is HJ = ħJ/4 σz(1) σz(2) In the measured magnetization spectrum of the spins, this leads to the splitting of the individual spin lines by frequency J, which we’ll now derive. We can write the magnetization of spin 1 as: <M1(t)> =...
  26. Danny Boy

    A General quantum measurements

    The following, regarding quantum measurement, is stated in the paper "Limitation on the amount of accessible information in a quantum channel" : "Our discussion of measurement will be based on a specific physical model of measurement, to which we now turn. Suppose we have a quantum system ##Q##...
  27. ExplosivePete

    Physics Is quantum information research well funded?

    I am applying to phd programs in physics right now. I am interested in doing research in quantum information science. I see there is a lot of interest and funding for quantum information science right now, but does anyone have any advice on whether or not this research will be well funded in the...
  28. DrHix

    How do I construct a controlled Hadamard gate?

    Homework Statement I am supposed to construct a controlled Hadamard gate using only single qubit and CNOT gates. Homework Equations [/B] We know that any arbitrary unitary Operator U can be written as the Martrix product U=AXBXC, where X is the NOT-Matrix and ABC=1 (identity matrix) I've...
  29. Q

    Physics Orienting myself toward quantum computing or a related field

    I am well aware that QC-related graduate programs are competitive so I am preparing myself for a rejection. Not because I'm unconfident. But because everyone should have a backup plan just in case. I haven't applied yet because I'm about to take the GRE. I really do enjoy both quantum physics...
  30. L

    Other Quantum Information and General Relativity

    Last year I've finished the undergraduate course in Mathematical-Physics and Mathematics and this year I've started on graduate school on Physics in order to obtain a master's degree. What I'm really interested are two main topics: general relativity and quantum field theory. I also like...
  31. A

    Programs Where can I do a masters in Quantum Mechanics?

    I am an undergraduate student in India doing my final year BS degree in Math. I am extremely interested in quantum mechanics and want to peruse quantum computation. What is the best possible course that I can take for my Masters? There appears to be a limited number of colleges that offer a...
  32. R

    I Energy conservation and information conservation

    How is information conserved when one form of energy is converted to other? Like how a black hole's gravitational energy is used to create photon pairs near the event horizon, what happens to the information in the gravitational wavepackets (gravitons?) and how is it not lost?
  33. P

    Prove relation for squeezed state - Quantum Information

    Homework Statement Prove the following relation for ##\zeta:=r e^{i \theta}##: S(\zeta)^\dagger a S(\zeta)= a \cosh r - a^\dagger e^{i \theta} \sinh r with ##S(\zeta)=e^{1/2[\zeta^\ast a^2-\zeta(a^\dagger)^2]}## and ##a## being the annihilation operator with eigenvalue ##\alpha##...
  34. E

    Displacement operator, squeeze operator - problem interpreting notation....

    Homework Statement Prove the following relations (for ##\zeta:=r e^{i\theta}##): \begin{align} D(\alpha)^\dagger a D(\alpha)&=a+\alpha\\ S(\zeta)^\dagger a S(\zeta)&= a \cosh r- a^ \dagger e^{i\theta} \sinh r \end{align} Homework Equations ##|\alpha\rangle## is the coherent state. ##a## and...
  35. Kiarash

    Fermi's Golden Rule

    Consider a system with countable quantum states. One can define Jij as the rate of transition of probability from i-th to j-th quantum state. In H-theorem, if one assumes both $$ H:=\Sigma_{i} p_{i}log(p_{i})$$ $$J_{ij}=J_{ji}$$ then they can prove the H always decrease. The latter is Fermi's...
  36. Domenico94

    Controlled - NOT gate

    Hi everyone. I'm just looking for schematics of cnot quantum gate, but on the Internet it only talks about it from a mathematical point of view. I want to ask you if you have some drawing, or schematics of it, from a "Physical" implementation, in the sense, how are the spins prepared, how we...
  37. EJC

    Schools Chances of Getting Into Graduate School Ph.D Programs

    I am a rising senior at a small liberal arts college, with an incredibly small (and therefore unrecognized) physics program. I am seeking advice regarding which Ph.D programs are within my reach. I plan on applying to AMO (Atomic, Molecular, and Optics) Ph.D programs with the intention of...
  38. Z

    Geometric measure of entanglement for fermions or bosons?

    For a system consisting of multiple components, say, a spin chain consisting ofN≥3spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner product between the wave function and a simple tensor product wave function. But it seems that none used this...
  39. AdityaDev

    Data storage in an SSD

    I am still in high school but my curiosity is not stopping me from posting in this forum. How is data stored in SSD? How does it differ from the old HDD? I heard that atoms are used to store data. How? Binary consists of 0 and 1. How does someone use an atom to represent 0 and 1? Does positive...